Now, suppose that the bottom of the tank described in problem #2 springs a leak. Toricelli's...

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Now, suppose that the bottom of the tank described in problem #2 springs a leak. Toricelli's law of hydrodynamics describes the fluid flow through the leak in terms of the size of the hole. If the base of the tank has area A and the hole has area H, then the fluid level in the tank, y(t), satisfies the separable first-order equation: dy dt Solve this equation. (Note: H, A, and g are constants.) H √√2gy When certain kinds of chemicals are combined to form a new compound, the rate at which the new compound is formed is modeled by the first-order separable ODE: dX dt =k(A-X)(B-X) where A and B represent the initial amounts of the reactants, X(t) is the amount of the new compound present at time t, and k is a constant that depends on the particular chemical reaction. Solve this equation for a chemical reaction in which A=B₁ Now, suppose that the bottom of the tank described in problem #2 springs a leak. Toricelli's law of hydrodynamics describes the fluid flow through the leak in terms of the size of the hole. If the base of the tank has area A and the hole has area H, then the fluid level in the tank, y(t), satisfies the separable first-order equation: dy dt Solve this equation. (Note: H, A, and g are constants.) H √√2gy When certain kinds of chemicals are combined to form a new compound, the rate at which the new compound is formed is modeled by the first-order separable ODE: dX dt =k(A-X)(B-X) where A and B represent the initial amounts of the reactants, X(t) is the amount of the new compound present at time t, and k is a constant that depends on the particular chemical reaction. Solve this equation for a chemical reaction in which A=B₁